Teachers at an East Harlem elementary school are bizarrely forbidden from communicating with parents without first getting a supervisor’s permission and from calling parents outside of normal school hours, the teachers handbook says.

While many schools are jumping through hoops to get parents involved in their kids’ education, PS 146 prohibits teachers from using their cellphones or personal e-mail accounts to discuss anything with parents of the students they oversee all day.

“All student concerns, phone calls to parents, any communication with parents/guardians and/or personnel matters require notification/approval to your direct supervisor,” the rigid regulations say. “ALL communication must be made from school phones only.”

The rules also oddly forbid teachers from using anything but their “full, legal” names in correspondence with students or parents.

“No initials or nicknames will be acceptable,” state the regulations — which some people say have put a damper on the school’s environment.

“When I was younger, my grandparents would just come in and talk to the teachers whenever they wanted . . . [teachers] would call parents at home and have conferences on the spot,” said Vanessa Hernandez, 25, a former student whose cousin is now enrolled. “Things have changed. It’s sad, because it hurts the children.”

Dr. Mona Silfen, the third-year principal of the C-rated school, said the policy had been in place before her arrival and that staffers can use their Department of Education e-mail addresses to reach out to parents with prior approval. She claimed the policy wasn’t strictly enforced — even though staffers told The Post they have to detail the time and nature of all phone calls to parents in a log book in the assistant principal’s office.

“Every school I’ve ever worked in, it was always the policy,” said Silfen.

After being shown the handbook, Department of Education officials said the school’s regulations on parent contact don’t conform to their policies.

“The rule outlined in this handbook is inappropriate, and we’ve asked the principal to remove it,” said DOE spokeswoman Deidrea Miller.

Ironically, the revelation of the school’s policy comes amid a push by Chancellor Cathie Black for schools to bolster parent engagement.

It also follows several black eyes suffered by the city’s parent-engagement office, particularly over its attempt to get school-based staffers involved in activities that supported Mayor Bloomberg’s political agenda.

DOE officials have said those efforts had been inappropriate and unauthorized.